According to Erik (Erik Lund a.k.a. Lens Doctor here), the focus shift correction function is implemented in the newer camera bodies at some point.
According to Jim Kasson's testing, this is not correct, at least for the D850:
https://blog.kasson.com/d850/d850-pdaf-tuning-and-focus-shift/However, I was told at the Nikon service here in Tokyo that the moodiness is caused by the fact that the neutral position of the SW motor will be off over time, and that you cannot correct it with the in-camera AF fine tuning. You need to have the lens re-calibrated machanically at Nikon service.
I don't understand how the motor could cause a systematic focus bias. The camera measures the phase difference and gives instructions to the focus motor to correct it. If in AF-C, then it will continually adjust the focus around the zero point. I can see that if the motor is not working correctly then there might be extra jitter.
I've had the same problem with my AF-S 50/1.8G and AF-S 24/1.8G, but after the calibration at Nikon service along with my camera body (D750 in my case), the problem was totally gone.
I tried having some of my lenses adjusted in service for AF and they said they tested them and were as good as they can be. No change distance dependent focus error. But, newer cameras have this much better handled in my experience; in the D800 I had large problems with distance dependent focus error, but D810 and D850 are ok in this respect. There may still be a small effect (like 1 point when going from 1 m to 30m distance) but I don't consider this to be a significant annoyance any more. With my D800 the 105DC required -20 at infinity and 0 up close. The D810 handled that lens fine at -12 across distances.
With the D810 and D5 I've followed the focus behavior of my lenses over the years, and once the fine tuning has been set correctly for a lens, I've never seen it drift over time. There may be a small adjustment needed over a range of distances or a small shift needed in changed lighting conditions (colour of artificial light) but over time, I've noticed no change. I realize that if the equipment is bumped then there may (and likely are) changes in the required fine tune settings but in normal use I don't find the values change over time.